Foundation Subject Research Articles

Widening participation and enhancing academic success: the impact of university diplomas on non-traditional students’ academic lives

University diplomas in Australia provide pathways into higher education for a diverse cohort of students, including students who do not meet the academic requirements of the bachelor course. Despite the role of university diplomas in widening participation and addressing inequities of access to higher education, there is a paucity of research about diplomas and diploma students. This mixed-method study investigated the experiences and outcomes of students entering higher education in Australia through university diplomas. Quantitative and qualitative findings showed that students found the diplomas to be beneficial for beginning their university study and their overall academic success. Students reported that the holistic support offered in the foundation subjects and across the institution was integral to their success. Students who completed university diplomas had higher success rates and GPAs in their subsequent bachelor courses compared to students who had not completed a diploma. Evidence from this research shows that university diplomas can help prepare students, particularly non-traditional university students, for success in academic study. A pedagogical design that incorporates transition pedagogy, includes and values adult learning principles, and allows for flexibility and independent learning is essential to support diploma students throughout their academic journey.

Development of blended learning media on similarity and congruence topics

Background: The integration of technology in education has become increasingly important in enhancing student engagement. Mathematics, as a foundational subject, often requires innovative approaches to improve students' problem-solving skills and conceptual understanding. Blended learning combines traditional and digital methods, offering a flexible and effective solution for teaching complex mathematical topics.Aim: This research aims to develop valid, practical, and effective learning media for teaching the topics of similarity and congruence, enabling students to better understand these mathematical concepts. The media is designed based on the Blended Learning approach.Method: The development process follows the Plomp model, which consists of three stages: (1) the initial investigation stage to identify needs and context, (2) the product development stage where the media is designed and refined, and (3) the assessment stage to evaluate its validity, practicality, and effectiveness.Results: The developed learning media was validated with a validity score of 86.99, categorized as very valid. It also achieved a practicality score of 87.01, indicating it is very practical, and an effectiveness score of 83.33, categorized as effective.Conclusion: Blended Learning-based media for teaching similarity and congruence is a valid, practical, and effective tool that can enhance students' understanding of the topics.

A Mathematical Problem Formulation Based on Number Theory

A branch of mathematics known as number theory is primarily concerned with the study of whole numbers. In that sense, number theory is used less in design than it is in analytics, computation, and other fields. Its inability to be used directly in any application was the issue. However, when combined with the computing power of modern PCs, number theory provides intriguing solutions to real-world issues. It serves a variety of functions in several industries, including computing, numerical analysis, and cryptography. The study of whole numbers is the primary focus of number theory. The fundamental structure of number theory has been gradually improved as a result of the dedication made by mathematicians throughout history to advancing the study of numbers, and as a result, a comprehensive and integrated field has been established. Number theory is a foundational subject that influences many other subjects and has a big impact on teachers. Number theory has been applied in statistics in a few fascinating ways. This overview paper's goal is to highlight particular noteworthy uses of this type. In number theory, indivisible numbers make up an interesting and challenging field of study. The main component of number theory is structured by diophantine equations. A Diophantine equation is an equation that needs necessary arrangements. This paper's first section looks at a few issues related to indivisible numbers and the function of Diophantine equations in Plan Theory. It is explained why Fibonacci and Lucas numbers commit to a semi-remaining Metis structure.

Research on the Optimization of Higher Mathematics Teaching Content Based on Vocational Demands

With the rapid development of the economy and technology, society has placed higher vocational-oriented requirements on higher education, especially in fields such as engineering and information technology. As a core foundational subject, higher mathematics must keep pace with the times to meet the practical needs for mathematical knowledge across different industries. However, the current teaching content of higher mathematics tends to be overly theoretical and disconnected from practical applications, making it difficult to adequately support students' career development. This study analyzes the requirements for mathematical knowledge in various industries from the perspective of vocational demands and proposes optimization strategies including modular design of teaching content and the integration of mathematics with vocational skills. It also explores innovative multidimensional teaching models and reforms in teaching evaluation systems. The findings provide a theoretical basis and practical guidance for the optimization of higher mathematics teaching content, contributing to the enhancement of students' professional abilities and employability.

Efficiency analysis of engineering classes: A DEA approach encompassing active learning and expositive classes towards quality education

The science, technology, engineering, and mathematics (STEM) education research delves into the core of sustainable development goals (SDGs), including the pillars of quality education (SDG4), robust economic growth (SDG8), and diminished inequalities (SDG10). These pursuits stand as keystones in sculpting inclusive societies and bridging societal gaps. While previous studies utilising data envelopment analysis (DEA) have explored educational performance mainly from a macro-perspective, there is a lack of micro-perspective investigation. Our study aims to fill this gap by proposing a DEA approach to assess the relative efficiency of engineering classes. We analysed 70 classes covering 38 subjects in the first semester of 2022 at a South American school. Methodologically, we employed the slack-based measure (SBM) model under the benefit of doubt (BoD) condition. Unlike prior research, we analysed classes' relative performance considering different pedagogical approaches - 11 active-learning classes (15.7 %) and 59 passive-learning classes (84.3 %). Our results showed that 18 classes were efficient (25.7 %). Active classes were more efficient, but few subjects maintained similar efficiencies for all classes. Moreover, efficient classes were concentrated in the last two years prior to graduation (57.9 %). This may represent an additional barrier for low-income students, who tend to drop out in the first years. The findings support several improvement recommendations, such as integrating digital technologies, boosting active learning opportunities, and bolstering classes in foundational subjects. Also, implications for researchers, decision- and policy-makers are discussed. Our approach can be replicated in diverse educational contexts, enabling the identification of strengths and weaknesses for more efficient educational management.

AI ethics should be mandatory for schoolchildren

AbstractAs society increasingly integrates artificial intelligence (AI) into its fabric, AI ethics education in primary schools becomes necessary. Drawing parallels between the integration of foundational subjects such as languages and mathematics and the pressing need for AI literacy, we argue for mandatory, age-appropriate AI education focusing on technical proficiency and ethical implications. Analogous to how sex and drug education prepare youth for real-world challenges and decisions, AI education is crucial for equipping students to navigate an AI-driven future responsibly. Our study delineates the ethical pillars, such as data privacy and unbiased algorithms, essential for students to grasp, and presents a framework for AI literacy integration in elementary schools. What is needed is a comprehensive, dynamic, and evidence-based approach to AI education, to prepare students for an AI-driven future.

Improving student success and retention in first-year nursing through embedded tutor support

BackgroundNursing students from diverse or equity backgrounds are less likely to possess the required skills to ensure success in their studies. This research explores the impact of embedded support on student learning in a first-year foundational subject, Contexts of Nursing, in an undergraduate nursing degree.t. MethodsThe Embedded Tutor Program offers specialised tutoring support for first-year undergraduate students. Embedded tutors, with backgrounds as registered nurses and academics, provided online one-on-one feedback to students on draft assessment tasks. Outreach contact was provided to students at risk of failing. A Pearson's Chi-squared test was used to assess the impact of tutor support on grade distribution and a paired student t-test was used to assess the difference in cumulative marks for students from equity backgrounds. Statistical significance was set at p < 0.05. Feedback provided by students, tutors and staff in an online anonymous survey was thematically analysed. ResultsThere was a significant grade shift for the 267 students who met with an embedded tutor (p < 0.05). Students who were a member of an Australian Government identified equity group had a significant increase in their cumulative mark if they met with a tutor of 9–17 % (p < 0.05). This improvement in cumulative mark was maintained for students with cumulative equity factors. The overwhelming majority of students who were identified as at risk of failing and met with a tutor following outreach support received a passing grade. Students reported growing skills and confidence in academic literacy was a key benefit of the program. ConclusionA shared approach to delivering education has a positive effect on the experience of learning. The combined efforts of the subject convenor, embedded tutors, and extended student service roles within the University resulted in outcomes that were positive for student learning. Determining student capacity for learning extended beyond a student's consideration of grades or their progression in the program to include the development of self-efficacy.

Transient response of doubly-curved bio-inspired composite shells resting on viscoelastic foundation subject to blast load using improved first-order shear theory and isogeometric approach

Investigating natural-inspired applications is a perennially appealing subject for scientists. The current increase in the speed of natural-origin structure growth may be linked to their superior mechanical properties and environmental resilience. Biological composite structures with helicoidal schemes and designs have remarkable capacities to absorb impact energy and withstand damage. However, there is a dearth of extensive study on the influence of fiber redirection and reorientation inside the matrix of a helicoid structure on its mechanical performance and reactivity. The present study aimed to explore the static and transient responses of a bio-inspired helicoid laminated composite (B-iHLC) shell under the influence of an explosive load using an isomorphic method. The structural integrity of the shell is maintained by a viscoelastic basis known as the Pasternak foundation, which encompasses two coefficients of stiffness and one coefficient of damping. The equilibrium equations governing shell dynamics are obtained by using Hamilton's principle and including the modified first-order shear theory, therefore obviating the need to employ a shear correction factor. The paper's model and approach are validated by doing numerical comparisons with respected publications. The findings of this study may be used in the construction of military and civilian infrastructure in situations when the structure is subjected to severe stresses that might potentially result in catastrophic collapse. The findings of this paper serve as the foundation for several other issues, including geometric optimization and the dynamic response of similar mechanical structures.

Enablers for accelerating biophilic design adoption in Australian buildings

Integrating biophilic design elements, such as green roofs and walls, has been proven to enhance the well-being of building occupants while boosting cities' ecological resilience. While many developed countries have acknowledged these benefits and are incorporating biophilic design principles into their new and refurbished buildings, Australia needs to catch up. This study aims to identify strategies to promote the integration of biophilic design in Australian buildings. To achieve this goal, semi-structured interviews were conducted with 24 architects and building sustainability consultants. The data was analysed using both manual and natural language processing techniques. The study uncovered nine strategies to accelerate the adoption of biophilic design, including making biophilic design a foundational subject in architectural and building sustainability education, enhancing building codes and regulations to mandate minimum biophilic features, demonstrating the business benefits of biophilic design to clients, embedding biophilic design as a core value in design organisations, and disseminating research and information on the cost-effective implementation of local vegetation for biophilic design. The study proposes a comprehensive framework for integrating nature into buildings, highlighting macro and micro enablers and their interactions. The findings offer practical strategies for stakeholders, including governments, design organisations, and professionals, to promote the adoption of biophilic design in Australia. Additionally, the study identifies opportunities to improve building design education and rating schemes to encourage the adoption of biophilic design.

Development of Interactive Learning Multimedia by Applying Contextual Teaching and Learning for Basic Graphic Design Subjects

The objectives of this study were to 1) create interactive learning multimedia materials by incorporating contextual teaching and learning to aid students in understanding graphic design topics for class X, 2) examine the viability of interactive learning multimedia by incorporating contextual teaching and learning to fundamental design subjects, and 3) assess the efficacy of using interactive learning multimedia by incorporating contextual teaching and learning. The three stages of this research's development-planning, design, and development are based on the Alessi and Trollip model. A total of 36 students from class X Multimedia 2 at SMK N 2 Sewon served as the research participants, while X Multimedia 1 served as the control group. gathering information through observation, questionnaires, learning product assessments, and learning accomplishment tests the findings revealed that: 1) Multimedia interactive learning materials for the foundational subject of graphic design in class X multimedia semester 2 at SMK N 2 Sewon were prepared. 2) Students (87.77%; "extremely feasible"), media professionals (94.18%), and material specialists (84.16%) rate the viability of learning media. (3) When contextual teaching and learning are applied, interactive learning media are said to be quite successful at improving student learning results.

A Brief Review of Anatomy Education in Korea, Encompassing Its Past, Present, and Future Direction.

Anatomy is a foundational subject in medicine and serves as its language. Hippocrates highlighted its importance, while Herophilus pioneered human dissection, earning him the title of the founder of anatomy. Vesalius later established modern anatomy, which has since evolved historically. In Korea, formal anatomy education for medical training began with the introduction of Western medicine during the late Joseon Dynasty. Before and after the Japanese occupation, anatomy education was conducted in the German style, and after liberation, it was maintained and developed by a small number of domestic anatomists. Medicine in Korea has grown alongside the country's rapid economic and social development. Today, 40 medical colleges produce world-class doctors to provide the best medical care service in the country. However, the societal demand for more doctors is growing in order to proactively address to challenges such as public healthcare issues, essential healthcare provision, regional medical service disparities, and an aging population. This study examines the history, current state, and challenges of anatomy education in Korea, emphasizing the availability of medical educators, support staff, and cadavers for gross anatomy instruction. While variations exist between Seoul and provincial medical colleges, each manages to deliver adequate education under challenging conditions. However, the rapid increase in medical student enrollment threatens to strain existing anatomy education resources, potentially compromising educational quality. To address these concerns, we propose strategies for training qualified gross anatomy educators, ensuring a sustainable cadaver supply, and enhancing infrastructure.

Analysis of Factors Influencing the Quality of Teaching Mathematics and Applied Mathematics under the Orientation of OBE Philosophy

Abstract Mathematics, recognized as a foundational subject, is marked by its high level of abstraction, rigorous logic, and extensive applicability, necessitating effective reforms. This article proposes a results-based teaching model for mathematics by integrating the Outcome-Based Education (OBE) concept with fundamental mathematical principles. The study utilizes a university in GD province as a case study to implement this OBE-based teaching model. Employing factor analysis and structural equation modeling, the research explores factors influencing the quality of teaching. Descriptive and correlational analyses were conducted on the variables involved, followed by structural equation modeling to test the proposed hypotheses. The findings revealed significant positive relationships among study habits, learning ability, interest motivation, learning resistance, teaching environment, and learning environment, with correlation coefficients positive at a 0.01 confidence level. The standardized path coefficients were 0.241, 0.143, 0.255, 0.153, 0.175, and 0.124 for learning habits, learning ability, interest motivation, learning resistance, teaching environment, and learning environment, respectively. These influences significantly and positively impact the effectiveness of the mathematics teaching model, demonstrating their beneficial effects on educational outcomes.

Groundwater Responses of Foundation Subjected to Water Level Fluctuation of Reservoir Considering Variability of Layered Structure

The effect of the variability in a layered structure, characterized by the spatial variability of the saturated hydraulic conductivity, on the distribution of a pressure head p in a foundation subjected to water level fluctuation in a reservoir is investigated with the aid of the random field theory, Karhunen–Loève (K-L) expansion, first-order moment approach, and cross-correlation analysis. The results show that the variability in the foundation structure has significant impacts on the groundwater response to the reservoir’s water level fluctuations. Regions with relatively large uncertainties of the p and σp values in the foundation are those around the initial water level at the reservoir side, and those at the distal end away from the reservoir. In addition, there is a larger variance of Ks, denoted as σlnKs2, a larger correlation scale in the horizontal direction λh, a larger correlation scale in the vertical direction λv, and a larger one-way time consumption of fluctuations T to a larger uncertainty in p. Moreover, the four factors (σlnKs2, λh, λv, and T) all have positive correlations with σp. σlnKs2 has the largest impact on σp in the foundation, λv has the second largest impact, and λh has the smallest impact. A foundation with small Ks values around the initial water level at the reservoir side and large Ks values around the highest water level at the reservoir side may produce larger p values in the foundation. These results yield useful insight into the effect of the variability in a layered structure on the distribution of the pressure head in a foundation subjected to water level fluctuation in a reservoir.

Student Perception of Knowledge and Skills in Pharmacology and Pharmacotherapy in a Bachelor’s Medical Curriculum

Background: Pharmacology and pharmacotherapy (P&amp;PT) is a foundational subject within the medical curriculum, preparing students for safe prescribing. The characteristics of students entering medical school change with time, and novel insights on teaching and learning also become available. A periodic review of the curriculum is required to investigate whether the current P&amp;PT teaching optimally supports learning. Methods: To investigate this, the students’ perceptions of their knowledge and competence in various P&amp;PT topics were studied. A total of 152 third-year bachelor’s students were invited to answer a 40-point online questionnaire. Results: The response rate for completing the questionnaire was 32% (N = 49). Students valued P&amp;PT teaching, did not skip P&amp;PT topics and desired more P&amp;PT classes. Interestingly, students were hesitant to use recommended literature and textbooks to prepare themselves for classes. Concerning perceptions of knowledge and competence, students rated lower confidence in prescription writing skills and knowledge of drugs acting on the central nervous system. Conclusions: Although there are many positive elements within the current curriculum, the incorporation of teaching methodologies to ensure active student engagement is warranted. These modifications are essential to properly training the current generation of medical students for their role as future prescribers. A relatively low response rate and overestimation of one’s competencies remain potential biases in the study.

A Bibliometric Exploration of Automation and its Impact on Mechanical Engineering Research

This bibliometric exploration delves into the dynamic landscape of automation's influence on mechanical engineering research. Leveraging the Scopus database and employing keyword search strategies targeting article titles, abstracts, and keywords from 1972 to 2022, this study examines the interdisciplinary nexus between automation and mechanical engineering. The top outcomes revealed a persistent focus on "mechanical engineering" as a foundational subject, fluctuating trends in thematic interests such as "control systems" and "robotics," and the pivotal roles of central authors within collaborative networks. Notably, collaboration networks identified influential figures like Wang X, Li D, and Zhang X, indicating their significant connections and influence within their respective networks. Future directions point toward deeper investigations into emerging themes like the convergence of information technology with automation, fostering global collaborations, and exploring correlations between academic output and real-world technological advancements. These findings underscore the dynamic and multifaceted nature of research within this field, paving the way for continued interdisciplinary exploration and innovation at the intersection of automation and mechanical engineering.

THE USE OF ELECTRONIC EDUCATIONAL RESOURCES IN TEACHING THE SUBJECT OF TECHNOLOGY METHODOLOGICAL FOUNDATIONS

Бул илимий макалада электрондук билим берүү ресурстарын (ЭББР) технология предметин окутуудагы колдонууда методологиялык негиздери изилденет, анын артыкчылыктарын, кыйынчылыктарын жана ишке ашырууда натыйжалуу стратегияларын изилдөөгө багытталат. Бүгүнкү санариптик доордо ЭББРды окутууга интеграциялоо барган сайын кеңири жайылып, салттуу класстык практикаларды жана педагогикалык ыкмаларды өзгөрттү. Айрыкча технология пред метинде, ЭББРды колдонуу, окутуу жана үйрөнүү тажрыйбаларын өркүндөтүү максатындагы жасалып жаткан жумуштар анализге алынат. Бул изилдөөнүн чөйрөсү ЭББРнын ар кандай түрлөрүн, анын ичинде онлайн маалымат базаларын, билим берүү программаларын, мультимедиа ресурстарын жана виртуалдык лабораторияларды изилдөөгө кирет. Бул ресурстарды технологиянын концепцияларын, принциптерин жана колдонмолорун окутууда жана үйрөнүүдө колдонууга басым жасалат, ал программалоо, роботтор, улуттук колориттеги санариптик дизайн, маалыматтык технологиялар сыяктуу жана башка ар кандай темаларды камтыйт. В данной научной статье исследуются методологические основы применения электронных образовательных ресурсов (ЭОР) в преподавании предмета технологии, основное внимание уделяется изучению его преимуществ, проблем и эффективных стратегий реализации. В сегодняшнюю цифровую эпоху интеграция ЭОР в обучение становится все более распространенной и меняет традиционные методы обучения в классе и педагогические подходы. В частности, в области технологий анализируется работа, выполняемая с целью улучшения практики использования, преподавания и обучения на основе приливов и отливов. Область этого исследования включает изучение различных типов приливов и отливов, включая онлайн-базы данных, образовательное программное обеспечение, мультимедийные ресурсы и виртуальные лаборатории. Основное внимание уделяется использованию этих ресурсов в преподавании и изучении технологических концепций, принципов и приложений, которые охватывают широкий спектр тем, таких как программирование, роботы, цифровой дизайн с национальным колоритом, информационные технологии и многое другое. This scientific article examines the methodological foundations of the use of electronic educational resources (EЕR) in teaching the subject of technology, focusing on the study of its advantages, problems and effective implementation strategies. In today's digital age, the integration of abbr into learning is becoming more widespread and changing traditional classroom teaching methods and pedagogical approaches. In particular, in the field of technology, the work carried out to improve the practice of using, teaching and learning on the basis of tides is analyzed. The field of this research includes the study of various types of tides, including online databases, educational software, multimedia resources and virtual laboratories. The main focus is on the use of these resources in teaching and learning technological concepts, principles and applications that cover a wide range of topics such as programming, robots, digital design with a national flavor, information technology and much more.

Risk Assessment of Offshore Wind Turbines Suction Bucket Foundation Subject to Multi-Hazard Events

For the offshore wind turbines (OWTs) located in a seismically active region, the occurrence of earthquakes combined with scour is a highly possible multi-hazard event. This study developed an alternative fragility analysis framework to assess the seismic performance of suction bucket-supported OWTs under the action of scour. First, the probabilistic approach was applied to calculate the occurrence probability of scour depth (SD) and earthquake events. Then, the possible combinations of these two events were considered in the analysis model to establish the fragility surface of the suction bucket foundation. Finally, by integrating the product of scour and earthquake hazard, as well as fragility curves, the suction bucket foundation failure probability was obtained. The developed framework provides a reliable approach to risk assessment for OWT-supporting structures in extreme event situations and can be applied to other complex natural hazards.

Education since 2010: Hirstian echoes

Abstract Although Paul Hirst was no longer working in the educational field between 2010 and 2020, echoes of his ideas resonate through the decade. I look at three examples. [1] The National Curriculum. In the 1990s Hirst had been critical of the newly introduced National Curriculum of 1988, built as it was around ten foundation subjects rather than practices of everyday life. While curricular reforms under the Labour governments of 1997–2010 came somewhat closer to his ideas, there has been a reversion since then to a subject-centred curriculum, with tests and examinations based on it much to the fore. But calls for more attention to social issues like climate change and ethnic diversity have Hirstian resonances, as have critical comments on the status quo from leading figures in politics and the inspectorate. [2] ‘Powerful knowledge.’ This notion, closely associated with the sociologist Michael Young, has been widely influential in educational circles since 2010. Its original definition in terms of bodies of knowledge with their own systems of concepts, is reminiscent of Hirst's celebrated and later abandoned ‘forms of knowledge’ theory. The paper speculates on possible biographical explanations of this commonality. [3] Teacher education. In 2017 HMCI Amanda Spielman commented on the need to improve teachers’ poor understanding of curriculum theory and notes that in the past it was better. This chimes with comments of Paul Hirst in 1994, although it is not clear how far Spielman would support his view that this work should first be rooted in practical teaching experience.

Analytical Study of High Speed Rail Bridge and Pile Foundation Subjected to Soil Structure Interaction Using Finite Element Software

High Speed Rail (HSR) was introduced in India in response to rising transport demand and reduced journey times. Pile foundation-supported piers are often used for elevated high-speed railways. The box-girder bridge and pile foundation embedded in multilayered soil have been analyzed for various critical conditions, viz. static condition, sudden brake conditions, derailment of train, and moving condition of train. In this type of complex problem, a theoretical approach to analyzing the pile foundation was insufficient. Thus, the Finite Element Method (FEM) based software, STAAD Pro. and PLAXIS 2D has been used. The main objective of this paper is to analyze the pile foundation under different conditions. Live loads on bridges are considered in Eurocode-1: Part 2. To perform the dynamic analysis, a 16 Hz frequency has been considered at a maximum 360 km/hr train speed. The results show that the moving condition and vibration effect increase the nodal displacement and in the case of derailment and sudden brake conditions, lateral load and moment have been increased, which changes the behavior of the pile foundation. According to IS 1343 code, a structure is safe as nodal displacement is within allowed limits in all cases. The combined effect of moving trains and vibrations increases nodal displacement by 10% when compared to the static condition. Hence, dynamic analysis is required. The lateral deflection of the pile increases in the case of sudden brake and derailment cases.

Ethnomathematical Study on Traditional Wedding Hantaran: 44-Fold Cloth from Lingga Regency

Several cultures in the Riau Islands Province are closely related to mathematics, but many people are unaware of this. Therefore, researchers are interested in further researching the mathematical practices found in the culture of Lingga Regency, Riau Islands, namely in making 44-fold cloth. There are indications of mathematical activities in making process of this traditional wedding hantaran. This research aims to describe the results of ethnomathematics research in making 44-fold cloth in Lingga, Riau Islands, including mathematical activities and concepts. This qualitative research uses an ethnographic approach. Data was collected through observations, interviews, and documentation to identify mathematical activities and concepts behind making 44-fold cloths. The researchers are the main instrument in this study. The data obtained from the instruments were analyzed based on data analysis for ethnographic qualitative research. The research results show embodied mathematical activities in making 44-fold cloth: measuring with standard units, folding with standard fold lines (axis of symmetry), and counting. Meanwhile, there are rooted mathematical concepts such as length measurement, plane figure, fold symmetry, rotation symmetry, angle, congruency, and basic numbers in making 44-fold cloth. This study suggests for using common occurrences to teach mathematics as a foundational subject before formal mathematics instruction.